Finite Group Databasebeta

← C5×#10427 #11933147

Subgroups — C5×#10427 #11933147

Order 1280.

460 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2820C211yesmaximal, characteristic
2C5×#1992C211yesmaximal, characteristic, complemented
3C5×#1959C211yesmaximal, characteristic
4C5×#1847C211yesmaximal, characteristic, complemented
5C2×C5×#330C211yesmaximal, characteristic, complemented
6C2×C5×#329C211yesmaximal, characteristic
7C5×#1295C211yesmaximal, characteristic, complemented
8C2×C5×#125C2211yescharacteristic
9C2×C5×#124C2211yescharacteristic
10C2×C5×#107—21no—
11C2×C5×#106—21no—
12C2×C5×#103—21no—
13C2×C5×#102—21no—
14C2×C5×#97C2211yescharacteristic
15C2×C5×#97C2211yescharacteristic
16C2×C5×#97C2211yescharacteristic
17C5×#399—21no—
18C5×#397—21no—
19C5×#396—21no—
20C5×#396—21no—
21C5×#395—21no—
22C5×#394—21no—
23C5×#384C2211yescharacteristic
24C5×#382C2211yescharacteristic
25C5×#340—21no—
26C5×#340—21no—
27C5×#330—22no—
28C5×#329—22no—
29#10427C511yesmaximal, characteristic, direct product factor, Sylow
30C22×C5×Q8D411yescharacteristic
31C22×C5×D4D411yescharacteristic
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C22×C5×C8—21no—
35C5×#125—21no—
36C5×#125—21no—
37C5×#125—21no—
38C5×#125—21no—
39C5×#124—21no—
40C5×#124—21no—
41C5×#124—21no—
42C5×#124—21no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4D411yescharacteristic
51C2×C5×C4⋊C4D411yescharacteristic
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C4⋊C4D411yescharacteristic
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C42×C5C2311yescharacteristic
61C5×#107—42no—
62C5×#106—42no—
63C5×#103—42no—
64C5×#102—42no—
65C5×#97—21no—
66C5×#97—21no—
67C5×#97—21no—
68C5×#97—21no—
69C5×#97—21no—
70C5×#97D412yes—
71C5×#95—21no—
72C5×#95—21no—
73C5×#95—21no—
74C5×#95—21no—
75#2820C2×C511yescharacteristic
76#1992C2×C511yescharacteristic, complemented
77#1959C2×C511yescharacteristic
78#1847C2×C511yescharacteristic, complemented
79C2×#330C2×C511yescharacteristic, complemented
80C2×#329C2×C511yescharacteristic
81#1295C2×C511yescharacteristic, complemented
82C24×C5—21no—
83C2×C5×Q8—21no—
84C2×C5×Q8—21no—
85C2×C5×Q8—41no—
86C2×C5×Q8—41no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—41no—
90C2×C5×D4—41no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—41no—
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5C2×D411yescharacteristic
99C22×C4×C5C2×D411yescharacteristic
100C2×C5×C8—22no—
101C2×C5×C8—22no—
102C2×C5×C8—22no—
103C2×C5×C8—22no—
104C2×C5×C8—22no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4—42no—
116C5×C4⋊C4—41no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—81no—
125C5×C4⋊C4—81no—
126C5×C22⋊C4—41no—
127C5×C22⋊C4—41no—
128C5×C22⋊C4—41no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4—81no—
131C5×C22⋊C4—81no—
132C5×C22⋊C4—81no—
133C5×C22⋊C4—81no—
134C42×C5C2×D411yescharacteristic
135C42×C5#4111yescharacteristic
136C42×C5#4111yescharacteristic
137C42×C5#4111yescharacteristic
138C2×#125C22×C511yescharacteristic
139C2×#124C22×C511yescharacteristic
140C2×#107—21no—
141C2×#106—21no—
142C2×#103—21no—
143C2×#102—21no—
144C2×#97C22×C511yescharacteristic
145C2×#97C22×C511yescharacteristic
146C2×#97C22×C511yescharacteristic
147#399—21no—
148#397—21no—
149#396—21no—
150#396—21no—
151#395—21no—
152#394—21no—
153#384C22×C511yescharacteristic
154#382C22×C511yescharacteristic
155#340—21no—
156#340—21no—
157#330—22no—
158#329—22no—
159C23×C5—41no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5—41no—
166C23×C5#12011yescharacteristic
167C5×Q8—42no—
168C5×Q8—81no—
169C5×D4—42no—
170C5×D4—81no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—81no—
193C2×C4×C5—81no—
194C2×C4×C5—81no—
195C2×C4×C5#12111yescharacteristic
196C2×C4×C5#12111yescharacteristic
197C2×C4×C5#12111yescharacteristic
198C2×C4×C5#12311yescharacteristic
199C2×C4×C5#12311yescharacteristic
200C2×C4×C5#12411yescharacteristic
201C5×C8—24no—
202C5×C8—42no—
203C5×C8—42no—
204C22×Q8C5×D411yescharacteristic
205C22×D4C5×D411yescharacteristic
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209#125—21no—
210#125—21no—
211#125—21no—
212#125—21no—
213#124—21no—
214#124—21no—
215#124—21no—
216#124—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C5×D411yescharacteristic
225C2×C4⋊C4C5×D411yescharacteristic
226C2×C4⋊C4C5×D411yescharacteristic
227C2×C4⋊C4C5×D411yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C42C23×C511yescharacteristic
235#107—42no—
236#106—42no—
237#103—42no—
238#102—42no—
239#97—21no—
240#97—21no—
241#97—21no—
242#97—21no—
243#97—21no—
244#97C5×D412yes—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249C22×C5—81no—
250C22×C5—81no—
251C22×C5—81no—
252C22×C5—81no—
253C22×C5—81no—
254C22×C5—81no—
255C22×C5—81no—
256C22×C5#39411yescharacteristic
257C22×C5#45311yescharacteristic
258C22×C5#45311yescharacteristic
259C22×C5#45411yescharacteristic
260C22×C5#45511yescharacteristic
261C22×C5#45611yescharacteristic
262C22×C5#45611yescharacteristic
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—81no—
270C4×C5—81no—
271C4×C5—81no—
272C4×C5—81no—
273C4×C5—81no—
274C4×C5—161no—
275C24—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4C2×C5×D411yescharacteristic
291C22×C4C2×C5×D411yescharacteristic
292C22×C4C2×C5×D411yescharacteristic
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—81no—
318C4⋊C4—81no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C42C2×C5×D411yescharacteristic
328C42C5×#4111yescharacteristic
329C42C5×#4111yescharacteristic
330C42C5×#4111yescharacteristic
331C2×C5—161no—
332C2×C5#165611yescharacteristic
333C2×C5#166011yescharacteristic
334C2×C5#166111yescharacteristic
335C2×C5#166411yescharacteristic
336C2×C5#203711yescharacteristic
337C2×C5#203811yescharacteristic
338C2×C5#203911yescharacteristic
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23C5×#12011yescharacteristic
347Q8—42no—
348Q8—81no—
349D4—42no—
350D4—81no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C5×#12111yescharacteristic
376C2×C4C5×#12111yescharacteristic
377C2×C4C5×#12111yescharacteristic
378C2×C4C5×#12311yescharacteristic
379C2×C4C5×#12311yescharacteristic
380C2×C4C5×#12411yescharacteristic
381C8—24no—
382C8—42no—
383C8—42no—
384C5#1042711yescharacteristic, direct product factor, Sylow
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C5×#39411yescharacteristic
393C22C5×#45311yescharacteristic
394C22C5×#45311yescharacteristic
395C22C5×#45411yescharacteristic
396C22C5×#45511yescharacteristic
397C22C5×#45611yescharacteristic
398C22C5×#45611yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—161no—
411C2—161no—
412C2C5×#165611yescharacteristic
413C2C5×#166011yescharacteristic
414C2C5×#166111yescharacteristic
415C2C5×#166411yescharacteristic
416C2C5×#203711yescharacteristic
417C2C5×#203811yescharacteristic
418C2C5×#203911yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C5×#1992C2semidirect
4. C5×#1847C2semidirect
5. C2×C5×#330C2semidirect
7. C5×#1295C2semidirect
29. #10427C5direct (N × H)
76. #1992C2×C5semidirect
78. #1847C2×C5semidirect
79. C2×#330C2×C5semidirect
81. #1295C2×C5semidirect
384. C5#10427direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#28202
C5×#19922
C5×#19592
C5×#18472
C2×C5×#3302
C2×C5×#3292
C5×#12952
#104275